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Quantum mnechanics with lagrangians?

  1. Mar 4, 2004 #1
    usually quantum mechanics is made with hamiltonians but..could it be done with lagrangians in the sense that LF=gF where F is the wave function and g plays a role of an eigenvalue what would happen with

    dq/dtF?..in fact would it be equal to qEnF where En is the energy..

    this can be useful for the case we have got a lagrangian but its HGamiltonian is H=0 so we can have some troubles it would be very useful for general relativity too......
  2. jcsd
  3. Mar 4, 2004 #2
    Certainly you can. Everything can be expressed as lagrangians. Quantum field theory is based on lagrangian mechanics, as are certain aspects of gravitation (the Einstein-Hilbert action).
  4. Mar 5, 2004 #3
    yes you can but you still have the problem of velocities..for example in Hamiltonian Formulation you have
    qF=qF and pF=-ihbardF/dx

    but in Lagrangian mechanics..you don,t have momenta but velocities and how could you cope with expresions of the form

    dq/dtF=?F perhaps that,s one of the main troubles of Lagrangian version of it....
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